PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systems

2025-07-09

AI Summary

This paper addresses the challenge of state estimation for nonlinear dynamical systems under partial observability and measurement noise. We propose a physics-informed neural network (PINN)-based adaptive observer framework that tightly integrates prior system dynamics with real-time sensor measurements—without requiring linearization or coordinate transformations—and achieves state reconstruction via joint optimization. Crucially, we embed the PINN directly into the observer architecture to adaptively learn time-varying gain matrices, and rigorously prove uniform ultimate boundedness (UUB) of the state estimation error. Evaluations on diverse nonlinear systems—including induction motors and satellite attitude dynamics—demonstrate that the proposed method significantly outperforms conventional approaches such as the extended Kalman filter (EKF) and unscented Kalman filter (UKF) in estimation accuracy, noise robustness, and adaptability to system variations.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Probabilistic Inference
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

State estimation for nonlinear dynamical systems is a critical challenge in control and engineering applications, particularly when only partial and noisy measurements are available. This paper introduces a novel Adaptive Physics-Informed Neural Network-based Observer (PINN-Obs) for accurate state estimation in nonlinear systems. Unlike traditional model-based observers, which require explicit system transformations or linearization, the proposed framework directly integrates system dynamics and sensor data into a physics-informed learning process. The observer adaptively learns an optimal gain matrix, ensuring convergence of the estimated states to the true system states. A rigorous theoretical analysis establishes formal convergence guarantees, demonstrating that the proposed approach achieves uniform error minimization under mild observability conditions. The effectiveness of PINN-Obs is validated through extensive numerical simulations on diverse nonlinear systems, including an induction motor model, a satellite motion system, and benchmark academic examples. Comparative experimental studies against existing observer designs highlight its superior accuracy, robustness, and adaptability.

Problem

• State estimation in nonlinear systems with partial noisy measurements
• Integrating system dynamics and sensor data via physics-informed learning
• Achieving accurate robust state estimation without system linearization

Innovation

• Adaptive Physics-Informed Neural Network observer
• Integrates system dynamics and sensor data
• Learns optimal gain matrix for convergence